Systems and methods for improved root mean square (RMS) measurement

ABSTRACT

Systems and methods are provided for improving the operation of a computer or other electronic device that utilizes root-mean-square (RMS) measurements, e.g., RMS current measurements, by reducing error in the RMS measurement. A series of measurement samples are received at a processor, which executes a noise-decorrelated RMS algorithm including: calculating a current-squared value for each measurement sample by multiplying the measurement sample by a prior measurement sample in the series (rather by simply squaring each measurement sample as in conventional techniques), summing the current-squared values, and calculating an RMS value based on the summed values. The processor may also execute a frequency-dependent magnitude correction filter to correct for frequency-dependent attenuation associated with the noise-decorrelated RMS algorithm. The calculated RMS value has a reduced error, particularly for lower-end current measurements, which may improve the operation of the computer or electronic device that utilizes the RMS value.

RELATED PATENT APPLICATION

This application claims priority to commonly owned U.S. ProvisionalPatent Application No. 62/579,437 filed Oct. 31, 2017, the entirecontents of which are hereby incorporated by reference for all purposes.

TECHNICAL FIELD

The present disclosure relates to current measurement, and moreparticularly, to systems and methods for improved RMS (root mean square)measurement, e.g., RMS current (I_(RMS)) measurement.

BACKGROUND

Conventional systems for measuring fundamental current componenttypically employ a metrology algorithm that compute RMS current byauto-correlating sampled current data (i.e., each datum is multiplied byitself) and then accumulating the auto-correlated data. Theauto-correlation increases the effect of noise in the sample, which mayprevent the ability to reduce or remove the noise by averaging. Suchtechniques may provide high error results at the lower end of currentmeasurement, due to the auto-correlated noise, e.g., incorporated in theI_x² term in the following equation for RMS current:

$\begin{matrix}{I_{{RMS\_}\; x} = {\sqrt{\frac{\sum\limits_{n = 1}^{N}{I\_ x}_{n}^{2}}{N}} = {{K\_ Ix} \times \sqrt{\frac{{ACC\_ I}{\_ x}}{N}}}}} & (1)\end{matrix}$

where I_(RMS_x) is the RMS current for a current sample stream, I_x_(n)represents each current measurement datum, N is the number of currentmeasurement samples, K_Ix represents a conversion scaling factor frominternal numeric units to outside world units (Amps), and ACC_I_xrepresents the internal metrology accumulator for I²-samples.

FIG. 1 illustrates example RMS current measurement error as a functionof current, for the following example parameters, using a conventionalRMS metrology technique (e.g., based on Equation 1):

-   -   Measurement using I²h [current-squared-hours] accumulator scaled        to 240 A maximum range;    -   Kt=0.075    -   t≥36 sec    -   24000:1 range

As shown, the measurement error increases greatly at the lower end ofcurrent measurement, as the percentage of the signal that is representedby noise increases with decreasing current.

BRIEF DESCRIPTION OF THE DRAWINGS

Example aspects of the present disclosure are described below inconjunction with the figures, in which:

FIG. 1 illustrates example RMS current measurement error as a functionof current, showing large measurement errors for lower current levels,using a conventional RMS measurement technique;

FIG. 2 shows an example algorithm for improved fundamental current RMSmeasurement, for improving the operation of a computer or otherelectronic device(s), according to an example embodiment of the presentinvention;

FIG. 3 is a pole-zero plot showing digital signal processing filter usedto provide frequency-dependent gain compensation filter of the examplealgorithm shown in FIG. 2, according to an example embodiment of theinvention;

FIG. 4 illustrates example test data for example embodiments of thepresent invention, showing a significant reduction in RMS currentmeasurement errors as compared with a conventional RMS measurementtechnique; and

FIG. 5 illustrates an example electronic device, e.g., a microcontrolleror microprocessor, that implements the example algorithm shown in FIG.2, e.g., embodied as firmware, for providing improved RMS currentmeasurement for improving the operation of the example electronic deviceand/or an associated computer or other electronic devices, according toone embodiment of the present invention.

SUMMARY

Embodiments of the present invention provide systems and methods areprovided for improving the operation of a computer or other electronicdevice that utilizes root-mean-square (RMS) measurements, by reducingerror in the RMS measurement. The disclosed concepts may apply to anytype of RMS measurements, such as current and voltage RMS measurements,for example. In the case of RMS current measurement, a series of currentmeasurement samples are received at a processor, which executes anoise-decorrelated RMS current algorithm including: calculating acurrent-squared value for each current measurement sample by multiplyingthe current measurement sample by a prior current measurement sample inthe series (rather by simply squaring each current measurement sample asin conventional techniques), summing the current-squared values, andcalculating an RMS current based on the summed values. The processor mayalso execute a frequency-dependent magnitude correction filter tocorrect for frequency-dependent attenuation associated with thenoise-decorrelated RMS algorithm. The calculated RMS current has areduced error, particularly for lower-end current measurements, whichmay improve the operation of the computer or electronic device thatutilizes the RMS current.

DETAILED DESCRIPTION

Embodiments of the present disclosure provide systems and methods forimproved measurement of RMS (root mean square) current, e.g., bycombining a present current sample stream with a delayed version of thecurrent sample stream. In some embodiments, each sampled current datumis multiplied by the current datum delayed by one sample to generateresulting I² samples for calculating a current RMS. Noise is therebydecorrelated between the two I² sample product terms, resulting in noisereduction through statistical averaging.

Thus, the inventive technique decorrelates noise of fundamental harmoniccurrent component measurement, I_(RMS_Fundamental). This decorrelationmay introduce a frequency-dependent attenuation; thus, some embodimentsmay include a frequency-dependent magnitude correction DSP filter tocorrect or compensate for such frequency-dependent attenuation. In someembodiments, this filter may be implemented to achieve pole and zeroplacement using a single multiplication and two additions, which mayguarantee a desired pole/zero placement to minimize or reduce noise dueto finite math effects. For example, in some embodiments, frequencyattenuation is corrected over a passband of interest [45, 66] Hz using asimple DSP filter implemented to ensure pole-zero stability.

Some embodiment may greatly reduce RMS measurement error for low-endcurrent measurement, as compared with conventional techniques, e.g., asdiscussed below in more detail (e.g., with reference to FIG. 4 discussedbelow).

FIG. 2 shows an example algorithm 10 for improved fundamental currentRMS measurement for improving the operation of a computer or otherelectronic device(s), according to an example embodiment of the presentinvention. Algorithm 10 may be implemented by any suitable hardware,software, firmware, or combination thereof. Some embodiments include amicroprocessor, memory, microcontroller, and/or other suitable devicesfor performing the data processing and/or data storage of the disclosedtechniques.

Example algorithm 10 includes a digital (DSP) frequency-dependent gaincorrection filter 20 and a noise-decorrelated RMS routine 30.Noise-decorrelated RMS routine 30 is designed to calculate an improvedRMS current (e.g., with reduced error especially for low-currentmeasurements), by decorrelating the noise in the current sample datathat is auto-correlated (and thus magnified) in the conventional RMSalgorithm. As this decorrelation may introduce a frequency-dependentattenuation (based on the relevant line frequency), thefrequency-dependent gain correction filter 20 is designed to correct forsuch frequency-dependent attenuation.

In some embodiments, the frequency-dependent attenuation introduced bythe disclosed decorrelation approach is a non-linear function of theratio of line frequency and the sampling frequency. Over thenarrow-bandwidth of interest that the fundamental line frequency isexpected to drift, for example, 45-66 Hz, filter 20 may be configuredcorrect the attenuation introduced by the decorrelation approach.

Referring to algorithm 10, a series of input current samples i(n)(sampled data proportional to current being measured) are received atthe frequency-dependent gain correction filter 20 from a source ofcurrent samples, e.g., a narrow-band filtered stream of current samplesfiltered to substantially remove harmonic content outside of thebandwidth of interest, for example frequencies outside of 45-66 Hz.Input current samples i(n) may be received at DSP filter 20 at asampling frequency, e.g., 4000 Hz. In the illustrated embodiment,frequency-dependent gain correction filter 20 comprises an infiniteimpulse response (IIR) filter and gain amplifier “g” configured togenerate a first intermediate output, i′(n), which pre-corrects forfrequency attenuation associated with the multiplication step performedin the noise-decorrelated RMS routine 30 (discussed below).

As shown in FIG. 2, the first intermediate output i′(n) generated bygain correction filter 20 is passed to noise-decorrelated RMS routine30, which multiplies each datum i′(n) output by gain correction filter20 with the datum delayed by one sample, i′(n−1), to providenoise-decorrelated current-squared samples defining a secondintermediate output i″(n). The second intermediate output i″(n) isaccumulated for “N” samples over an integral number of half cycles ofthe line frequency to produce the final output, Σi″². This final outputvalue may then be used in the conventional manner to calculate theI_(RMS_Fundamental) value (fundamental harmonic RMS current) using theequation: I_(RMS)=sqrt(Σi″²/N).

The values for the constant “k” and gain factor “g” in thefrequency-dependent gain correction filter 20 may have any suitablestatic or dynamic values, and determined in any suitable manner foroptimized or desired results, e.g., based on the line frequency and/orcurrent sampling frequency. In one example embodiment for a linefrequency band of [45, 66] Hz and a 4 KHz sampling frequency, optimalconstant values are determined and set as k=0.217143 and g=1.5547492444.Other frequency-dependent filters may be implemented in otherembodiment, e.g., based on the particular application of the algorithm.

FIG. 3 is an example pole-zero plot 50 showing stability provided by theexample frequency-dependent gain correction filter 20 shown in FIG. 2,and using the example values discussed above, according to an exampleembodiment.

Thus, based on the above, embodiments of the invention may allow adirect computation of I_(RMS_Fundamental), based on the conventionalconcept of using the I²-samples accumulator, and also maintainsignificant accuracy at very low end of current range (e.g., 24000:1).

One embodiment has been tested for an example measurement at 10 mA(using a maximum 240 A meter). A conventional I_(RMS) calculationprovided 25.386 mA, which represents a 153.857% error. An I_(RMS)calculation using example algorithm 10 shown in FIG. 2 provided 9.879mA, which represents an error of only −1.214%. In addition, testingshows that the response across entire of fundamental line frequencypassband [45, 66] Hz is flat to less than 0.001%.

Some embodiment may greatly reduce current RMS measurement error, ascompared with conventional techniques. For example, system and methodsaccording to the present invention can reduce RMS measurement errorpercentage by a factor of at least 2, at least 5, at least 10, or atleast 100. Some embodiments may reduce RMS measurement error from anerror of greater than 200% (provided by a conventional technique formeasuring RMS current) to less than 2% for low-current RMS measurements.

FIG. 4 illustrates example test data for one example embodiment of thepresent invention, showing a significant reduction in RMS currentmeasurement errors as compared with a conventional RMS measurementtechnique. FIG. 4 shows error rates provided by (a) a conventionalfull-bandwidth approach (“Normal_FBW”), a FBW (Full Band Width)de-correlated noise approach (“Decorrelated_FBW”), and a NBW (NarrowBand Width) de-correlated noise approach (“Decorrelated_NBW”). As shown,both the FBW and NBW de-correlated noise approach provide a noticeablenoise reduction from the conventional FBW approach. In particular, theexample FBW de-correlated noise approach reduced noise by about half,while the example NBW de-correlated noise approach reduced noise byabout or more than a factor of 10 for the tested current levels. Thus,this example embodiment provides a noticeable error reduction for theFBW approach, and even a greater error reduction for NBW measurements.

Embodiments of the invention can be incorporated or used in any suitablecomputers or electronic devices or products, e.g., incorporated in themetrology firmware on a microcontroller or a dual-core ARM Cortex M4processor, for example.

FIG. 5 illustrates an example electronic device 100, e.g., a computer orother electronic device, that implements the example algorithm 10 shownin FIG. 2 for providing improved RMS measurement, e.g., RMS currentmeasurement, for improving the operation of the example electronicdevice 100, one or more components of the electronic device 100, and/oran associated computer or other electronic devices, according to oneembodiment of the present invention.

As shown, electronic device 100 may include a memory device 120, aprocessor 130 (e.g., a microprocessor), and one or more electroniccomponents or circuitry 140. The example RMS algorithm 10 shown in FIG.2 or other similar RMS algorithm may be embodied in firmware 110 inmemory device 120 (e.g., flash ROM) and executable by processor 130 forproviding improved RMS measurement, e.g., improved RMS currentmeasurement for a current within or associated with electronic device100. In other embodiments, RMS algorithm 10 may be embodied in softwarestored in a suitable memory device 120 and executable by processor 130.The improved RMS measurement, e.g., RMS current measurement, may be usedby electronic component(s) or circuitry 140 to thereby providereduced-error measurement values (e.g., reduced-error RMS currentvalues) to thereby improve the operation of component(s)/circuitry 140.In some embodiments, processor 120 and memory 120 storing RMS algorithm10 (and in some embodiments, component(s)/circuitry 140 that utilizesthe improved RMS measurements) may be embodied in a microcontroller.

Embodiments of the systems and methods (algorithms) disclosed herein mayprovide one or more technical advantages. Traditional RMS calculationssquare each datum and sum the squared terms. This doubles the noise dueto auto-correlation of the noise. Embodiments of the present inventionde-correlate the noise to significantly improve the RMS measurement,especially at the low end of the measurement range where the noise iscommensurate with signal or larger than the signal. Thus, the disclosedsystems and methods may allow dramatically improved accuracy for RMScurrent measurement, especially at the low-end of the current range, andthus provide extended range current measurement. In addition, thedisclosed systems and methods may be simple to implement with littleadditional added DSP overhead. The systems and methods may allowstraditional calculation method of I_(RMS_Fundamental) component, and mayallow accurate pulse measurement of I²-hr_Fundamental quantities at lowrates using standard meter test equipment.

The invention claimed is:
 1. A method for improving the operation of acomputer or other electronic device that utilizes root-mean-square (RMS)measurements, by reducing error in the RMS measurement, the methodcomprising: receiving, at a processor of the computer or otherelectronic device, a series of measurement samples; executing, by theprocessor, a noise-decorrelated RMS algorithm including: for eachreceived measurement sample, calculating an adjusted sample value by amathematical combination step comprising multiplying each respectivemeasurement sample by a prior measurement sample in the sequence; andsumming the adjusted sample values for the sequence of measurementsamples; and calculating an RMS value based on the summed adjustedsample values; executing, by the processor, a frequency-dependentmagnitude correction filter to the series of measurement samples tocorrect for a frequency-dependent attenuation associated with thenoise-decorrelated RMS algorithm; and controlling at least one componentof the computer or other electronic device based on the calculated RMSvalue.
 2. The method of claim 1, wherein the series of measurementsamples comprise a series of current measurement samples, and the RMSvalue calculated by execution of the noise-decorrelated RMS algorithm isan RMS current value.
 3. The method of claim 1, wherein multiplying eachrespective measurement sample by a prior measurement sample in thesequence comprises multiplying each received measurement sample by theimmediately previous measurement sample in the sequence to calculate acurrent-squared value.
 4. The method of claim 1, wherein thefrequency-dependent magnitude correction filter comprises an infiniteimpulse response (IIR) filter.
 5. The method of claim 1, comprisingexecuting the frequency-dependent magnitude correction filter for eachmeasurement sample prior to executing the noise-decorrelated RMSalgorithm for each respective received measurement sample.
 6. The methodof claim 1, wherein the frequency-dependent magnitude correction filteris configured to achieve a stable pole and zero placement using a singlemultiplication and two additions.
 7. The method of claim 1, wherein thecomputer or other electronic device that utilizes root-mean-square (RMS)measurements comprises a microcontroller.
 8. The method of claim 1,wherein the computer or other electronic device that utilizesroot-mean-square (RMS) measurements comprises a microprocessor.
 9. Themethod of claim 1, wherein the computer or other electronic device thatutilizes root-mean-square (RMS) measurements comprises a computerincluding at least one microcontroller or microprocessor.
 10. A systemfor improving the operation of a computer or other electronic devicethat utilizes root-mean-square (RMS) measurements, by reducing error inthe RMS current, the system comprising: a memory device storing anoise-decorrelated RMS algorithm; and a processor configured to: receivea series of measurement samples; and execute the noise-decorrelated RMSalgorithm including: for each received measurement sample, calculatingan adjusted sample value by a mathematical combination step comprisingmultiplying each respective measurement sample by a prior measurementsample in the sequence; and summing the adjusted sample values for thesequence of measurement samples; and calculating the RMS value based onthe summed adjusted sample values; and execute a frequency-dependentmagnitude correction filter to the series of measurement samples tocorrect for a frequency-dependent attenuation associated with thenoise-decorrelated RMS algorithm.
 11. The system of claim 10, whereinthe series of measurement samples comprise a series of currentmeasurement samples, and the RMS value calculated by execution of thenoise-decorrelated RMS algorithm is an RMS current value.
 12. The systemof claim 10, wherein the processor is integrated in a microcontroller.13. The system of claim 10, wherein the processor comprises amicroprocessor.
 14. The system of claim 10, wherein multiplying eachrespective measurement sample by a prior measurement sample in thesequence multiplying each received measurement sample by the immediatelyprevious measurement sample in the sequence to calculate acurrent-squared value.
 15. The system of claim 10, wherein thefrequency-dependent magnitude correction filter comprises an infiniteimpulse response (IIR) filter.
 16. The system of claim 10, wherein theprocessor is configured to execute the frequency-dependent magnitudecorrection filter for each measurement sample prior to executing thenoise-decorrelated RMS algorithm for each respective receivedmeasurement sample.
 17. The system of claim 10, wherein thefrequency-dependent magnitude correction filter is configured to achievea stable pole and zero placement using a single multiplication and twoadditions.
 18. A method for improving the operation of a computer orother electronic device that utilizes root-mean-square (RMS)measurements, by reducing error in the RMS measurement, the methodcomprising: receiving, at a processor of the computer or otherelectronic device, a series of measurement samples; executing, by theprocessor, a noise-decorrelated RMS algorithm to calculate RMS valuesfrom the series of measurement samples, the noise-decorrelated RMSalgorithm including: a noise-decorrelated RMS routine that decorrelatesnoise in the measurement samples; and a frequency-dependent gaincorrection filter that corrects for frequency-dependent attenuationintroduced by the noise-decorrelated RMS routine; wherein thefrequency-dependent gain correction filter precedes thenoise-decorrelated RMS routine in the noise-decorrelated RMS algorithm;controlling at least one component of the computer or other electronicdevice based on the calculated RMS values.
 19. The method of claim 18,wherein the noise-decorrelated RMS routine includes multiplying eachmeasurement sample in the series of measurement samples by a priormeasurement sample in the series of measurement samples.